Abstract. This paper discussed the development of one - step, one hybrid block method
for the solution of first order initial value problems. Two functions were
combined to form the basis function which is collocated and interpolated at
some selected grid and off-grid points to develop a linear multistep method
which is implemented in block form. The paper further investigated the
properties of the block method and found it to be convergent. The region of
absolute stability was also investigated. The method was tested on some
numerical experiments and found to give better approximation than the
methods we compared our results with.